1

Complete the table for the following proportional relationships.

1. A student reads 52 pages per hour. 2. A babysitter makes $8.50 per hour

Explain whether the following graphs are proportional or non-proportional.

3. 4.

_________________________________ ________________________________

_________________________________ ________________________________

Find the constant and write an equation in the form y = kx.

5. 6.

_________________________________ ________________________________

How does a graph show a proportional relationship?

______________________________________________________________________________

Hours Pages

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Hours Pages

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5

468

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Constant of Proportionality

2

The graph below show the relationship between time and distance run by two horses.

1. Explain what the point (0,0) ____________________________________________________

2. How long does it take each horse to run one mile?

______________________________________________________________________________

______________________________________________________________________________

3. Write an equation for the relationship between time and distance for each horse.

Horse A Horse B

__________________________________ ___________________________________

4. How far would each horse run in 12 minutes

Horse A Horse B

__________________________________ ___________________________________

5. Bargain DVDs cost $5 each at Mega Movie.

Graph the proportional relationship.

Give two ordered pairs and explain its meaning .

______________________________________

______________________________________

3

Independent Practice

1. Three tickets to attend an Off-Broadway show cost $81, 4 tickets cost $108, and 5 tickets cost $135.

a. Show that the relationship between number and the cost is a proportional relationship by making a table of tickets for 1 to 5 tickets.

b. The constant of proportionality k is _________________

. c. Write an equation for the relationship: _________________

2. On the seventh-grade trip to Washington, D.C., for every 8 students, there were 3 chaperones. Twelve chaperones were needed. How many students went on the trip?

______________________________________________________________________________

Determine whether the relationship is a proportional relationship. If so, write an equation for the relationship, and tell what each of your variables represents. If the relationship is not proportional, explain. 3. Ty takes 1 hour to read 35 pages, 2 hours to read 70 pages, and 3 hours to read 105 pages.

______________________________________________________________________________

4. There are 12 grams of protein in 2 ounces of almonds.

______________________________________________________________________________

5. __________________________

6.

__________________________

4

Complete each table. Explain why the relationship is a proportional relationship.

1. A cashier earns $8 per hour. 2. Tomatoes cost $0.70 per pound.

Tell whether the relationship is a proportional relationship. Explain your answer. 3. 4.

The graph shows the relationship between the distance traveled by a car and the amount of fuel used by the car. 5. Explain the meaning of (2, 40). 6. Write an equation for this relationship. 7. Suppose a compact car uses 1 gallon of fuel for every 27 miles traveled. How would the graph for

the compact car compare to the graph for the car shown?

8. Two companies offer digital cable television as described below.

Company A: $39.99 per month with no installation fee

Company B: $34.99 per month with a $50 installation fee

For each company, tell whether the relationship between months of service and total cost is a proportional relationship. Explain why or why not.

5

Find each unit rate. Show work and confirm answer with a calculator.

1. Julie walks 3½ miles in 1¼ hours. 2. Kenny reads

page in

minute.

3. A garden snail moves

foot in

hour. 4. A fertilizer cover

square foot in

hour.

Find each unit rate. Determine which is lower.

5. Brand A: 240 mg sodium

pickle 6. Ingredient C: ¼ cup for

serving

Brand B: 325 mg sodium ½ pickle Ingredient D:

cup for

serving

7. The information for 2 pay-as-you-go cell phone companies is given.

What is the unit rate in dollars per hour for each company?

Which company offers the best deal?

Another company offers $.05 per minute. How would you find the unit rate per hour? 8. Terrance and Jesse are training for a long-distance race. Terrance trains at a rate of 6 miles every

half hour, and Jesse trains at a rate of 2 miles every 15 minutes.

What is the unit rate in miles per hour for each runner?

How long will each person take to run a total of 50 miles at the given rate?

Sandra runs at a rate of 8 miles in 45 minutes. How does her unit rate compare to Terrance’s and to Jesse’s?

Unit Rate

6

Independent Practice 1. To make 2 batches of nut bars, Jayda needs to use 4 eggs. How many eggs are used in each batch of

nut bars? 2. On her way to visit her parents, Jennifer drives 265 miles in 5 hours. What is her average rate of

speed in miles per hour? 3. Last week Alexander was paid $56 for 7 hours of work. How much money does Alexander’s job pay

per hour?

4. Ned has scored 84 points in the first 6 games of the basketball season. How many points per game has Ned scored?

5. At the local grocery store, a 16-ounce bottle of apple juice costs $3.20. What is the cost of the

apple juice per ounce?

6. An above-ground swimming pool is leaking. After ½ hour the pool has leaked

of a gallon of

water. How many gallons of water per hour is the swimming pool leaking?

7. After ¾ of a minute a sloth has moved just

of a foot. What is the sloth’s speed in feet per

minute? 8. Food A contains 150 calories in ¾ of a serving. Food B contains 250 calories in 2/3 of a serving. Find

each unit rate. Which food has fewer calories per serving?

7

1. If the relationship between distance y in feet and time x in seconds is proportional, which rate is

represented by

= .6?

Show why you chose this answer.

2. The Brine family makes regular monthly deposits in a savings account. The graph shows the

relationship between the number x of months and the amount y in dollars in the account.

What is the amount of money the family saves per month?

Write an equation in the form y = mx to represent this graph.

3. A store had a sale on art supplies. The price p of each item was marked down 60%. Which

expression represents the new price? Explain your reasoning.

4. In which equation is the constant of proportionality 5?

5. A baker is looking for a recipe that has the lowest unit rate for flour per batch of muffins. Which

recipe should she use?

Constant of Proportionality & Unit Rate HW

8

6. Suri earns extra money by dog walking. She charges $6.25 to walk a dog once a day 5 days a week

and $8.75 to walk a dog once a day 7 days a week. Write an equation (y = mx) to represent the daily

charge for this situation.

7. Kevin was able to type 2 pages in 5 minutes, 3 pages in 7.5 minutes, and 5 pages in 12.5 minutes.

Which equation represents the number of minutes (y) it takes to read (x) pages?

8. Randy walks ½ mile each 1/5 hour. How far will Randy walk in one hour?

9. The table shows how far several animals can travel at their maximum speed in a given time.

a. Write each animal’s speed as a unit rate in feet per second.

b. Which animal has the fastest speed?

10. The table shows the proportional relationship between Juan’s pay and hours he works. Complete

the table. Plot the data and connect the points with a line

9

1. Pete’s blueprint shows a layout of a house. Every 4 inches

represents 24 feet. One of the walls is 24 inches. What is the

actual length of the wall?

The side wall is 16 inches. What is the actual length in feet?

If the back wall is actually 33 feet, what is the length of the wall

on the blueprint?

2. The art class is planning to paint a mural on an outside wall. This figure is a scale drawing of the

wall. The scale is 2 in. : 3 ft. What is the area of the actual wall?

3. Find the length and width of the actual room, shown in the scale drawing. Then find the area of the

actual room. Round your answer to the nearest tenth.

4. The drawing plan for an art studio shows a rectangle that is 13.2 inches by 6 inches. The scale is 3

inches = 5 feet. Find the length and width of the actual studio. Then find the area of both the scale

drawing and the actual studio.

Scale Drawings

10

Independent Practice 1. The plan of a terrace is shown at right. The scale is 2 inches : 6 feet. What are the length and width

of the terrace? Find the terrace’s area. Length: _________________

Width: __________________

Area: ___________________ 2. A scale drawing of a patio is shown at right. The scale is 4 inches : 6.8 feet. What are the length and

width of the patio? Find the patio’s area.

Length: _________________

Width: __________________

Area: ___________________ 3. The scale for a scale drawing is 8 millimeters : 1 centimeter. Which is larger, the actual object or the

scale drawing? Explain. 4. Carol has a small copy of a painting. The dimensions of her copy are shown at right. The scale of the

copy is 0.5 inches : 12 centimeter.

a. Find the dimensions of the original painting. b. Find the area of the original painting.

4. On a scale drawing, a bookshelf is 8 inches tall. The scale factor is

. What is the height of the

bookshelf?

5. On a scale drawing, a school is 1.6 feet tall. The scale factor is

. Find the height of the school.

11

Find the circumference and area of each circle below.

7. A circular patio has a diameter of 35 yards. What is the circumference of the patio?

Write your answer in terms of and to the nearest tenth. 8. A paper plate has a diameter of 10 inches. What is the area of the plate?

Write your answer in terms of and to the nearest tenth. 9. A circular light fixture has a radius of 20 centimeters. What is the circumference of the light fixture? .

Write your answer in terms of and to the nearest tenth.

Circles

12

1. In the scale of a park, the scale is 1 cm: 10 m. Find the area of the actual park.

2. Find the circumference and area of each circle a) in terms of and b) to the nearest tenth.

3. On a map with a scale of 2 cm = 1 km, the distance from Ben’s house to the beach is 4.6

centimeters. What is the actual distance?

4. A group of students is designing a triangular banner to hang in the school gym. They first draw a

design on paper. The triangle has a base of 5 inches and a height of 7 inches. If 1 inch on the

drawing is equivalent to 1.5 feet on the actual banner, what will the area of the actual banner be?

5. A forest ranger wants to determine the radius of the trunk of a tree. She measures the

circumference to be 8.6 feet. What is the trunks radius to the nearest tenth of a foot?

6. A studio apartment has a floor that measures 80 feet by 64 feet. A scale drawing of the floor on

grid paper uses a scale of 1 unit : 8 feet. What are the dimensions of the scale drawing?

7. The plan of a terrace is shown at right. The scale is

4 inches : 7 feet. What are the length and width of the terrace? Find the terrace’s area.

Length: ____________ Width: ______________ Area: ________________

Scale Drawing and Circles HW

13

Find the percent increase.

1. From $5 to $8 2. From 20 students to 30 students

3. From 86 books to 150 books 4. From $3.49 to $3.89

5. Nathan usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per

day. If he starts drinking 64 ounces, what is the percent increase? Round to the nearest percent.

6. From $80 to $64 7. From 95 to 68

8. From 16 bagels to 0 bagels 9. From 145 pounds to 132 pounds

10. Over the summer, Jackie played video games 3 hours per day. When school began in the fall, she was

only allowed to play video games for half an hour per day. What is the percent decrease? Round to the

nearest percent.

Percents

14

Find the new amount given the original amount and the percent of change.

1. $9; 10% increase 2. 48 cookies; 25% decrease

3. 340 pages; 20% decrease 4. $29,000; 4% decrease

5. Adam currently runs about 20 miles per week, and he wants to increase his weekly mileage by 30%.

How many miles will Adam run per week?

Independent Practice

1. Complete the table below

2. The bar graph shows the number of hurricanes in the Atlantic Basin from 2006 – 2011.

Find the amount of change and the percent of decrease in the number

of hurricanes from 2008 to 2009 and from 2010 to 2011.

Compare the percents of decrease.

Between which two years is the percent change the greatest?

What was the percent change?

Percents

15

1. To make a profit, stores mark up the prices o the items they sell. A sports store buys skateboards

from a supplier for s dollars. What is the retail price for skateboards that the manager buys for $35

and $56 after a 42% markup?

2. A discount store marks down all of its holiday merchandise by 20% off the regular selling price. Find

the discounted price of the decorations that regularly sell for $16 and $23.

3. Marcus buys a varsity jacket from a clothing store. The price of the jacket is $80 and the sales tax is

8%. What is the total cost of the jacket?

Total Price = Sale Price + Sales Tax

= p + .08p

= 1.08p

4. Martin finds a shirt on sale for 15% off at a department store. The original price was $20. Martin must

also pay 8.5% sales tax.

How much is the shirt before sales tax is applied?

How much is the shirt after taxes are applied?

Percents

16

Independent Practice

Rachel’s co-worker made price tags for several items that are to be marked down by 35%. Match each Regular

Price to the correct Sale Price, if possible. Not all sales tag match an item.

A B C D E

2. Harold works at a men’s clothing store, which marks up its retail clothing 27%. The store purchases

pants for $74, suit jackets for $325, and dress shirts for $48. How much will Harold charge a customer

for 2 pairs of pants, 3 dresses and a suit jacket?

3. Grant marks down some $2.49 pens to $1.99 for a week and then marks them back up to $2.49. Find the

percent decrease and increase to the nearest percent. Are the percent changes the same? If not, which

is greater?

4.

17

1. Terry deposits $200 into a bank account that earns 3% simple interest per

year. What is the total amount in the account after 2 years?

Write the percent as a decimal ___________ Then use the formula I = Prt

2. Arial borrows $400 on a 4 year loan. She is charged 5% simple interest per year. How much interest is

she charged for 4 years? What is the total amount she has to pay back?

Write the percent as a decimal ___________ Then use the formula I = Prt

3. Emily’s meal costs $32.75 and Darren’s meal costs $39.98. Emily treats Darren by paying for both meals,

and leaves a 14% tip. Find the total cost.

4. Ken earns a monthly salary of $2,200 plus a 3.75% commission on the amount of his sales at a men’s

clothing store. What would he earn this month if he sold $4,500 in clothing? Round to the nearest cent.

5. Nora makes $3,000 a month. The circle graph shows how she spends her money. How much money

does Nora spend on each category?

Simple Interest

18

Percent Homework

1. The original price of a barbecue grill is $79.50. The grill is marked down 15%. What is the sale price

of the grill?

2. A bank offers an annual simple interest rate of 8% on home improvement loans. Tobias borrowed

$17,000 over a period of 2 years. How much did he repay altogether?

3. The sales tax rate in Jan’s town is 7.5%. If she buys 3 lamps for $23.59 each and a sofa for $769.99,

how much sales tax does she owe?

4. The day after a national holiday, decorations were marked down 40%. Before the holiday, a

patriotic banner cost $5.75. How much did the banner cost after the holiday?

5. Find the percent change from 72 to 90. Is this an increase or decrease?

6. A bank offers a home improvement loan with simple interest at an annual rate of 12%. James

borrows $14,000 over a period of 3 years. How much will he pay back altogether?

7. What is 18% of 350?

19

8. If the sale price of a pair of jeans is $12 and the original price was $25. What is the discount as a

percent?

9. If the sales tax is $2.80 on a $35 video game what is the sales tax rate?

10. The sale price of an MP3 player is $42.50. If the discount was 15%, what was the original price of

the MP3 player?

11. You went to dinner with 3 friends and each of your meals was $8.99.

a. What is the total of the 4 meals?

b. You add a 20% tip. What is the tip to the nearest dollar?

c. What was the total of the meal? What does each person owe?

12. You purchased a microwave for you dorm room at college. The original price was $79. You have a

coupon for 25% off. What is the sale price?

The tax rate is 8.5%. What is the total cost of the microwave after the discount and sales tax?

20

1. –8 + (–6) 2. – 4 + (– 7) 3. – 9 + (– 12)

4. 5 + (– 2) 5. – 10 + 4 6. – 15 + 8

7. 2 – 9 8. – 3 – (–4) 9. 11 – (–12)

10. A bus stops at 2:30, letting off 15 people and letting on 9 people. The bus makes another stop ten

minutes later to let off 4 more people. How does the number of people on the bus after the second stop

compare to the number of people on the bus before the 2:30 stop.

11. Cate and Elena were playing a card game. The stack of cards in the middle had 24 cards in it to begin

with. Cate added 8 cards to the stack. Elena then took 12 cards from the stack. Finally, Cate took 9 cards

from the stack. How many cards were left in the stack?

12. Which expression has the same value as – 3 + (–5) 13. Which of the following has the

greatest value?

14. A diver’s elevation is 30 feet below sea level. She dives down 12 feet. What is her elevation after the

dive?

15. The temperature was –3° . The temperature then dropped 11 degrees. What is the new temperature?

16. Which number line models the expression – 3 + 5

Adding and Subtracting Integers

21

1. –1(9) 2. 14(–2) 3. (–9)( –6)

4. –2(50) 5. –4(15) 6. –18(0)

7. –7 (–7) 8. –15(9) 9. 8(–12)

10. –3(–100) 11. 0(–153) 12. –6(32)

13. Flora made 7 withdrawls of $75 each from her bank account. What was the overall change in her

account?

14. A football team lost 5 yards on each of 3 plays. Explain how you could us a number line to find the

team’s change in field position after the 3 plays.

15. The temperature dropped 2°F every hour for 6 hours. What was the total number of degrees the

temperature changed in the 6 hours?

16. The price of one share in Company ABC declined $5 per day for 4 days in a row. How much did the price

change in total after the 4 days?

17. A mountain climber down a cliff 50 feet at a time. He did this 5 times in one day. What was the overall

change in his elevation?

18. When Brooke buys lunch at the cafeteria, money is withdrawn

from a lunch account. The table shows amounts withdrawn in

one week. By how much did the amount in Brooke’s lunch account

change by the end of that week?

Multiplying Integers

22

Find the quotient

1.

2. 21 ÷ 3.

4. 0 ÷ 4 5.

6. 30 ÷ 10

7.

8. 31 ÷ ( 31) 9.

10.

11. 84 ÷ 7 12.

13. 14.

15. 0 ÷ 0

16. Clark made four of his truck payments late and was fined four late fees. The total change to his

savings from late –$40. How much was one late fee.

17. Jan received –22 points on her exam. She got 11 questions wrong out of 50 questions. How much

was Jan penalized for each wrong answer?

18. Allen’s score in a video game was changed by –75 points because he missed some targets. He got –

15 points for each missed target. How many targets did he miss?

19. Louisa’s savings change by –$9 each time she goes bowline. In all, it changed by –$108 during the

summer. How many times did she go bowling in the summer?

20. Elise withdrew $20 at a time from her bank account and withdrew a total of $140. Frank withdrew

$45 a time from his bank account and withdrew a total of $270. Who made the greater number of

withdrawls?

Dividing Integers

23

Independent Practice

1. –6(–5) + 12 2. 3(–6) – 3 3. –2(8) + 7

4. 4(–13) + 20 5. –4(0) – 4 6. –3(–5) – 16

7. Bella pays 7 payments of $5 each to a game store. She returns one game and receives $20 back.

What is the change to the amound of money she has.

8. Ron lost 10 points seven times playing a video game. He then lost an additional 100 points for going

over the time limit. What was the total change in his score?

9. Ned took a test with 25 questions. He lost 4 points for each of the 6 questions he got wrong and

earned an additional 10 points for answering a bonus question correctly. How many points did Ned

receive or lose overall?

10. Mr. Harris has some money in his wallet. He pays the babysitter $12 an hour for 4 hours of

babysitting. His wife give him $10, and he puts the money in his wallet. By how much does the

amount in his wallet change?

Evaluate and compare the following by using a < , >, or =.

11. –3(–2) + 3 _________ 3(–4) +9 12. –8(–2) – 20 _________ 3(–2) + 2

13. –7(5) – 9 _________ –3(20) + 10 14. –16(0) – 3 __________ –8(–2) – 3

24

Integer Homework

1. A diver is – 18 feet relative to sea level. The diver descends to an undersea cave that is 4 times as far from

the surface. What is the elevation of the cave?

2. A football team lost 4 yards on 2 plays in a row. Write a number that represents the change in field

position?

3. Clayton climbed down 50 meters. He climbed down in 10 meter intervals. In how many intervals did

Clayton make his climb?

4. Clara played a video game before she left the house to go on a walk. She started with 0 points, lost 6 points

3 times, won 4 points, and lost 2 points. How many points did she have when she left the house to go on

the walk?

5. Which expression is equal to 0? 6. Which expression results in a negative

answer?

7. Rochelle and Dana started with the same amount of money in their bank accounts. Rochelle made three

withdrawals of $25 and then wrote $100 check. Dana deposited $5 and then wrote a $200 check.

a. Find the total change in the amount of money in Rochelle’s account.

b. Find the total change in the amount of money in Dana’s account.

25

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. 11

11.

12.

Find the sum.

13. –3 + (–1.5) 14. 1.5 + 3.5 15. –1.5 + 4

16. 2.75 + (– 8) + (– 5.25) 17. 4.5 + (–12) + (–4.5)

18. –3 + ( 1

+ ( 2

19. - 8 +

20.

21.

22. A submarine submerged at a depth of –35.25 meters dives an additional 8.5 meters. What is the new

depth of the submarine.

23. Renee hiked for 4

miles. After resting, Renee hiked back along the same route for 3

miles. How many

more miles does Renee need to hike to return to the place where she started?

Fractions

26

1. 3 –(– 8) 2. –3

3. –7 – 4

4. – 0.5 – 3.5 5. – 14 – 22 6. –12.5 – (–4.8)

7.

(

) 8. 65 – (–14) 9. 24

(

)

10. A girl is snorkeling 1 meter below sea level and then dives down another .5 meters. How far below the sea

level is the girl?

11. The first play of a football game resulted in a loss of 12 ½ yard. Then a penalty resulted in another loss of 5

yards. What is the total loss or gain?

12. Eleni withdrew $45.00 from her savings account. She then used her debit card to buy groceries for $30.15.

What was the total amount Eleni took out of her account?

13. How much deeper is the deepest canyon on Mars than the deepest canyon on Venus?

14. What is the difference between Earth’s highest mountain and its deepest ocean canyon?

What is the difference between Mars’ highest mountain and its deepest canyon?

Which difference is greater? How much greater is it?

Integers, Fractions, & Decimals

27

1. 5(–

2. 3(

3. –3

4. –

– 5. 4(–3) 6. –1.8(5)

7. –2(–3.4) 8. .54(8) 9. –5(1.2)

10.

11.

12.

13.

14. The price of one share of a company declined $3.50 per day for 4 days in a row. What is the overall change

in price of one share?

15. In one day, 18 people each withdrew $100 from an ATM machine. What is the overall change in the amount

of money in the ATM machine?

Integers, Fractions, & Decimals

28

Integer, Fraction, & Decimal Homework

1. Jamie had $37 in his bank account on Sunday. The table shows his account activity for the next four

days. What was the balance in Jaime’s account after the deposit on Thursday?

2. Working together, 6 friends pick

pounds of pecans at a pecan farm. They divide the pecans

equally among themselves. How many pounds does each friend get?

3. A used motorcycle is on sale for $3,600. Erik makes an offer equal to ¾ of this price. How

much does Erik offer for the motorcycle? 4. What is the value of (– 3.25)( – 1.56)?

5. Mrs. Rodriguez is going to use 6

yards of material to make two dresses. The larger dress requires

3

yards of material. How much material will Mrs. Rodriguez have left to use on the smaller dress?

6. Ruby at 1/3 of a pizza, and Angie ate 1/5 of the pizza. How much of the pizza did they eat in all?

29

7. Wendy buys 1.2 pounds of bananas. The bananas cost $1.29 per pound. To the nearest cent, how

much does Wendy pay for the bananas? 8. Lila graphed the points – 2 and 2 on a number line. What is the distance between these two points? 9. A scuba diver at a depth of -12 feet (12 ft below sea level), dives down to a coral reef that is 33.5

times the diver’s original depth. What is the diver’s new depth? 10. The school Spirit Club spent $320.82 on food and took in $643.59 selling the food. How much did

the Spirit Club make? 11. The temperature was -10°F and dropped 16°F Which statement represents the resulting

temperature in degrees Fahrenheit?

12. Juanita is watering her lawn using the water stored in her rainwater tank. The water level in the

tanks drops

inch every 10 minutes she waters.

What is the change in the tank’s water level after 1 hour?

What is the expected change in the tank’s water level after 2.24 hours?

30

Write impossible, unlikely, equally likely, likely, or certain.

1. Randomly picking a green card from a standard deck of playing cards.

2. Picking a red from a standard deck of playing cards

3. Picking a number less than 15 from a bag with papers numbered 1 to 12.

4. Picking a number that is divisible by 5 from a jar with papers labeled from 1 to 12.

Find the probability.

5. Spinning a spinner that has 5 equal sections marked 1 – 5 and landing on an even number number.

6. Picking a diamond from a standard deck of playing cards which as 13 cards in each of 4 suits: spades, hearts,

diamonds, and clubs.

7. What is the probability of not rollwing a 5 on a standard number cube?

8. There are 4 queens in a deck of 52 cards. What is the probability of not selecting a queen?

9. A spinner has 5 equal sections marked 1 through 5. What is the probability of not landing on 4?

10. A spinner has 3 equal sections that are red, white, and blue. What is the probabiltiy of not landing on blue?

11. There are 12 pieces of fruit in a bowl. Seven apples and 2 are peaches. What is the probability that a randomly

selected piece of fruit will not be an apple or peach?

12. For breakfast, Clarissa can choose from oatmeal, cereal, French toast, or scrambled eggs. She thinks that if she

selects a breakfast at random, it is likely to be oatmeal. Is she correct?

13. A garden contains 90 sweet pea plants, which have either purple or white flowers. About 70 have purple and

about 20 have white. Would you expect that one plant randomly selected from the garden will have purple or

white?

Probability

31

1. A spinner has three unequal sections: red, yellow and blue. The table shows the results of Nolan’s spins.

Find the experimental probability of landing on each color.

2. Martin has a bag of marbles. He removed one marble at random, recorded the color and then placed it

back in the bag. He repeated the process several times and recorded the results. Find the experimental

probability of drawing each color.

3. A spinner has four sections lettered A, B, C, and D. The table shows the result of several spins. Find the

experimental probability of spinning each letter as a fraction in simplest form, a decimal, and a percent

4. The names of the students in Mr. Hayes’ math class are written on the board. He then writes each name on

an index card and shuffles the cards. Each day he randomly draws a card, and the chosen student explains a

math problem at the board. What is the probability that Ryan is chosen today? What is the probability that

Ryan is not chosen today?

Probability

32

1. A food truck serves chicken and records the order size and sides on their orders. What is the probability

that the next order is for 3-piece with cole slaw?

2. Drink sales for an afternoon at the school carnival were recorded in the table. What is the experimental

probability that the next drink is a small cocoa?

Simulations

At a street intersection, a vehicle is classified either as a car or a truck, and it can turn left, right, or go straight.

About an equal number of cars and trucks go through the intersection and turn in each direction. Use a simulation

to find the experimental probability that the next vehicle will be a car that turns right.

A coin was tossed to represent a car or truck – Head = Car and Tails = Truck

The spinner represents the direction the vehicle turns.

There are 6 possible outcomes:

Based on the simulation conducted what is the probability that a car turns right?

Compare this to what you would expect the outcome to be…

Probability

33

1. A baseball player reaches first base 30% of the times he is at bat. Out of 50 times at bat, about how many

times will the play reach first base?

2. The experimental probability that it will rain on any given day in Houston, Texas is about 15%. Out of 365

days, about how many days can residents predict rain?

3. A catalog store as 6% of its orders returned for a refund. The owner predicts that a new candle will have

812 returns out of the 16,824 sold. Do you agree with this prediction?

4. On a toy assembly line, 3% of the toys are found to be defective. The quality control officer predicts that

872 toys will be found defective out of 24,850 toys made. DO you agree with this prediction?

5. A litght-rail service claims to be on time 98% of the time. Jeanette takes the light-rail 40 times one month,

how many times can she predict she will be on time? Is the light-rail’s claim accurate if she is late 6 times?

6. On average, a college claims to accept 18% of its applications. If the college has 5,000 applicants, predict

how many will be accepted. If 885 applicants are accepted, is the college’s claim accurate?

7. The table shows the number of student at the beginning of the year and the percentage that can be

expected to move out of the area by the end of the year.

How many 7th graders are expected to move?

If 12 students actually moved, is this more or less than what was

expected?

Probability

34

1. At a school fair, you have a choice of spinning Spinner A or Spinner B. You win a prize if the spinner lands on

a section with a star in it. Which spinner should you choose if you want a better chance of winning?

2. At a school fair, you have a choice of randomly picking a ball from Basket A or Basket B. Basket A has 5

green balls, 3 red balls, and 8 yellow balls. Basket B has 7 green balls, 4 red balls, and 9 yellow balls. You can

win a video game if you pick a red ball.

Complete the chart.

Which basket would give you the better chance

of winning?

3. A jar contains 4 cherry cough drops and 10 honey cough drops. What is the probability you choose a cherry

cough drop?

4. You choose a movie CD at random from a case containing 8 comedy CDs, 5 science fiction CDs, and 7

adventure CDs. Find the probability the CD is not a comedy.

5. You roll a number cube. What is the probability the number you roll is greater than 2 and less than 5?

35

Independent Practice

1. Find the number of possible outcomes.

Find the probability of choosing a Turkey and Swiss

on wheat bread.

2. Complete the tree diagram and make a list to find the sample space.

3. Nate is getting dressed. He considers two different shirts, three pairs of pants, and three pairs of shoes. He

chooses one of each of the articles at random. Draw a tree diagram.

Shirt Pant Shoes

What is the probability that he will wear jeans and not sneakers?

What is the probability that he will wear t-shirt and shorts?

C K S

T J F

H D

36

Probability HW

Find the probability of each event.

1. Rolling a 5 on a fair number cube.

2. Picking a blue marble from a bag of 4 red marbles, 6 blue marbles, and 1 white marble.

3. Rolling a number greater than 7 on a 12-sided number cube.

4. Picking a 7 from a standard deck of cards. A standard deck includes 4 cards of each number from 2

to 10.

5. Christopher picked coins randomly from his piggy bank and got the numbers of coins shown in the

table. Find each experimental probability.

The next coin picked is a quarter. __________

The next coin picked is not a quarter. __________

The next coin picked is a penny or a nickel. __________

6. A grocery store manager found that 54% of customers usually bring their own bags. In one

afternoon, 82 out of 124 customers brought their own grocery bags. Did a greater or lesser number

of people than usual bring their own bags?

7. A store has a sale bin of soup cans. There are 6 cans of chicken noodle soup, 8 cans of split pea

soup, 8 cans of minestrone, and 13 cans of vegetable soup. Find the probability of picking each type

of soup at random. Then predict what kind of soup a customer is most likely to pick.

37

8. Patty tosses a coin and rolls a number cube.

a. Find the probability that the coin lands on heads and the cube lands on an even number.

b. Patty tosses the coin and rolls the number cube 60 times. Predict how many times the coin will land on heads and the cube will land on an even number.

9. Sam tossed 4 coins at the same time. She did this 50 times, and 6 of those times, all 4 coins showed

the same result (heads or tails).

a. Find the experimental probability that all 4 coins show the same result when tossed.

b. Can you determine the experimental probability that no coin shows heads? Explain.

c. Suppose Sinead tosses the coins 125 more times. Use experimental probability to predict the number of times that all 4 coins will show heads or tails. Show your work.

10. A pizza parlor offers thin, thick, and traditional style pizza crusts. You can get pepperoni, beef,

mushrooms, olives, or peppers for toppings. You order a one-topping pizza. How many outcomes

are in the sample space?

11. During the month of April, Dora kept track of the bugs she saw in her garden. She saw a ladybug on

23 days of the month. What is the experimental probability that she will see a ladybug on May 1?

12. For breakfast, Trevor has a choice of 3 types Make a tree diagram to find the sample space.

of bagels (plain, sesame, or multigrain), 2 types of eggs (scrambled or poached), and 2 juices (orange or apple).

38

Biased or Random?

1. The student council puts pieces of paper with the names of all the seventh graders in a bag and selects 20

names.

2. Members of a polling organization survey 700 of the 7,453 registered voters in a town by randomly

choosing names from a list of all registered voters.

3. Carol wants to find out the favorite foods of students at her middle school. She asks the boys’ basketball

team about their favorite foods.

4. Dallas wants to know what elective subjects the students at his school like best. He surveys students who

are leaving band class.

5. Determine which sampling method will better represent the entire population. Justify your answer.

6. Rose asked students on the bus line how many books they had in their back packs. She recorded the data as

a list: 2, 6, 1, 0, 4, 1, 4 , 2, 2. Make a dot plot for the books carried by this sample of students.

Statistics

39

7. The number of pets owned by a random sample of students at Park Middle School is shown below. Use the

data to make a box plot.

9 2 0 4 6 3 3 2 5

Order the data from least to greatest.

8. A shipment to a warehouse consists of 3,500 MP3 players. The manager chooses a random sample of 50

MP3 players and finds that 3 are defective. How many MP3 players in the shipment are like to be defective?

Find the median and the mode of the data.

1. 11, 17, 7, 6, 7, 5, 15, 9 2. 43, 37, 49, 51, 56, 40, 44, 50, 36

Find the mean of the data

3. 9, 16, 13, 14, 10, 16, 17, 9 4. 108, 95, 104, 96, 97, 106, 94

40

4. The dot plots show the heights of 15 high school basketball players and the heights of 15 high school

softball players.

Visually compare the shapes of the dot plots. Visually compare the centers of the dot plots.

Visually compare the spreads of the dot plots.

5. The number of points a high school basketball player scored during the games he played this season are

organized in the box plot shown.

Find the least and greatest values.

Least: __________________ Greatest ________________

Find the median and describe what it means for the data.

Find and describe the lower and upper quartiles.

The interquartile range is the difference between the upper and lower quartiles. Find the interquartile

range.

41

6. Numerically compare the dot plots of the number of hours a class of students exercise each week to

the number of hours they play video games each week.

Compare the shapes of the dot plots.

Compare the centers of the dot plots by find the medians.

Compare the spreads of the dot plots by calculating the range.

7. Use the box plot Terrance created for his math test scores. Find each value.

Minimum _____________

Maximum ____________

Range __________ IQR __________

8. Use the box plots showing the distribution of the heights of hockey and volleyball players.

Which group has a greater median height? ___________________

Which group has the shortest player? _______________________

Which group has an interquartile range about about 10? __________________________

42

9. Which is a true statement based on the dot plots below?

10. The dot plot shows the lengths of a random sample of words in a 4th grade book and a 7th grade book.

Compare the shapes. Compare the ranges.

11. The tables show the numbers of miles run by the students in two classes.

For each class, what is the mean? What is the mean absolute deviation?

The difference of the means is about ____________ times the mean of the absolute deviations.

43

Independent Practice

1. The tables show the number of minutes per day students in a class spend exercising and playing video

games. What is the difference of the means as a multiple of the mean absolute deviations?

Find the difference in the means. Write the difference of the means as a multiple of the

mean absolute deviations.

2. The high jumps in inches of the students on two intramural track and field teams are shown below. What is

the difference of the means as a multiple of the mean absolute deviations?

The difference of the means is about ____________ times the mean of the absolute deviations.

3. Part of the population of 4,500 elk at a wildlife preserve is infected with a parasite. A random sample of 50

elk shows 8 are infected. How many elk are like to be infected?

4. A dot plot includes all of the actual data values. Does a box plot include any of the actual data values?

44

5. Patrons in the children’s section of a local branch library were randomly selected and asked their ages. The

librarian wants to use the data to infer the ages of all patrons of the children’s section so he can select age

appropriate activities. In 3 – 6, complete each inference.

7 4 7 5 4 10 11 6 7 4

Make a dot plot of the sample population data.

Make a box plot of the sample population.

7 4 7 5 4 10 11 6 7 4

a. The most common ages of children that use the library are ________ and ________.

b. The range of ages of children that use the library is from ________ to ________.

c. The median age of the children that use the library is ________.

6. A manufacturer fills an order for 4,200 smart phones. The quality inspector selects a random sample of 60

phones and finds that 4 are defective. How many smart phones in the order are likely to be defective?

45

Statistics HW

1. Molly uses the school directory to select, at random, 25 students from her school for a survey on

which sports people like to watch on television. She calls the students and asks them, “Do you think

basketball is the best sport to watch on television?”

a. Did Molly survey a random or biased sample?

b. Was the question asked an unbiased question?

2. There are 2,300 licensed dogs in Clarkson. A random sample of 50 of the dogs in Clarkson shows

that 8 have ID microchips implanted. How many dogs in Clarkson are likely to have ID microchips

implanted?

3. A store gets a shipment of 500 MP3 players. Twenty-five of the players are defective, and the rest

are working. A graphing calculator is used to generate 20 random numbers to simulate a random

sample of the players.

Let numbers 1 – 25 represent players that are ____________________________

Let numbers 21 – 500 represent players that are __________________________

How many players in this sample are expected to be defected?

If 300 players are chosen at random from the shipment, how many are expected to be defective

based on the sample? Does the sample provide a reasonable inference?

46

4. The dot plots show the number of hours a group of students spends online each week, and how

many hours they spend reading. Compare the dot plots.

Shape Spread

Center

Calculate the medians. Calculate the ranges.

5. The tables show the typical number of minutes spent exercising each week for a group of 4th grade

students and a group of seventh-grade students.

What is the mean number of minutes spent exercising for 4th graders? For seventh graders?

What is the mean absolute deviation of each data set?

6. Which is a true statement based on the box plots below?

47

7. A survey asked 100 students in a school to the name the temperature at which they feel most comfortable.

The box plot below shows the results for temperature in degrees Fahrenheit. Which could you infer based

on the box plot below?

8. The average times (in minutes) a group of students spends studying and watching TV per school day

are given.

a. Find the mean times for studying and for watching TV.

b. Find the mean absolute deviations (MADs) for each data set.

c. Find the difference of the means as a multiple of the MAD, to two decimal places?

d. Create box and whisker for Studying and Watching TV.

48

1. Jill and Kyle get paid per project. Jill is paid a project fee of $25 plus $10 per hour. Kyle is paid a project fee

of $18 plus $14 per hour. Write an expression to represent how much a company will pay to hire both to

work the same number of hours.

2. A company rents out 15 food booths and 20 game booths at the county fair. The fee for a food booth is

$100 plus $5 per day. The fee for a game is $50 plus $7 per day. The fair lasts for d days, and all the booths

are rented for the entire time. Write and simplify an expression for the amount in dollars that the company

is paid.

3. A rug maker is using a pattern that is a rectangle with a length of 96 inches and a width of 60 inches. The

rug maker wants to increase each dimension by a different amount.Let l and w be the increases in inches of

th the length and width. Write and simplify an expression for the perimeter of the new pattern.

4. The perimeter of the figure is given. Find the length of the indicated side.

5.

Write an expression for the perimeter of each court.

Write an expression that describes how much great the perimeter of the basketball court is than the

perimeter of the tennis court?

Suppose the tennis court is 36 feet wide. Find all dimensions of the two courts.

Algebra

49

Solve each equation.

1. 4.9 + z = – 9 2. r – 17.1 = – 4.8 3. –3c = 36

4. A scuba diver is exploring at an elevation of – 12.2 meters. As the diver rises to the surface, she plans to

stop and rest briefly at a reef that has an elevation of –4.55 meters. Find the vertical distance that the diver

will travel.

x represents the vertical distance between her initial elevation and the elevation of the reef.

5. How many degrees warmer is the average

temperature in November than in January?

6. Suppose that during one period of extreme cold, the average daily temperature decreased 1 ½° F each day.

How many days did it take for the temperature to decrease by 9° F.

7. Billy has a gift card with a $150 balance. He buys several video games that cost $35 each. After the

purchases, his gift card balance is $45. Write an equation to help find out how many video games Billy

bought.

50

8. A school bought $548 in basketball equipment and uniforms costing $29.50 each. The total cost was

$2,023. Write an equation you can use to find the number of uniforms the school purchased.

9. Heather has $500 in her savings account. She withdraws $20 per week for gas. Write an equation Heather

can use to see how many weeks it will take her to have a balance of $220.

10. A restaurant sells a coffee refill mug for $6.75. Each refill costs $1.25. Last month Keith spent $31.75 on a

mug and refills. Write an equation you can use to find the number of refills that Keith bought.

11. There are 172 South American animals in the Springdale Zoo. That is 45 more than half the number of

African animals in the zoo. Write an equation you could use to find n, the number of African animals in the

zoo.

12. To convert a temperature from degrees Fahrenheit to degrees Celcius, first subtract 32. Then multiply the

result by

. An outdoor thermometer showed a temperature of – 10 °C. What was the temperature in

degree Fahrenheit?

13. 9s + 3 = 57 14. – 3y + 12 = – 48

51

Independent Practice

1.

2. – 17 +

3. 7(c – 12) = –21 4. 46 = –6t – 8

5. After making a deposit, Paul had $264 in her savings account. She noticed that if she added $26 to

the amount originally in the account and doubled the sum, she would get the new amount. How

much did she originally have in the account?

6. The current temperature in Smalltown is 20 F. This is 6 degrees less than twice the temperature that

it was six hours ago. What was the temperature in Smalltown six hours ago?

7. Archie noticed that if he takes the opposite of his age and adds 40, he gets the number 28. How old

is Archie?

8. Seth has 11 more than twice as many customers as when he started selling newspapers. He now has

73 customers. How many did he have when he started?

52

Solve and graph the following.

1. 2.

3. 4.

5. 7.

8. A barge can safely haul no more than 400 tons across the river. The barge has an empty weight of

24 tons. The average weight of the railroad cars is 4 tons each. How many railroad cars can the

barge haul?

9. Fifty students are trying to raise at least $12,500 for a class trip. They have already raised $1,250.

How much should each student raise, on average, in order to meet the goal? Write and solve the

two-step inequality for this problem.

10. An employee of a car wash earns $12 for each car she washes. She always saves $60 of her weekly

earnings. This week, she wants to have at least $100 in spending money. What is the fewest

number of cars she must wash?

53

Algebra Homework

1. Which expression is equivalent to (9x –

) – (7x +

)

2. A taxi costs $1.65 for the first mile and $.85 for each additional mile. Which equation could be

solved to find the number x of additional miles traveled in a taxi given that the total cost of the trip

$20.

3. Timothy began the week with $35. He bought lunch at school, paying $2.25 for each meal. Let x be

the number of meals he bought at school and y be the amount of money he had left at the end of

the week. Write and solve an equation to represent the situation.

4. A sales tax of 6% is added to the price of an item. If Marisa buys an item, which expression indicates

how much she will pay in all? Explain:

5. Which expression factors to 8(x + 2)?

6. Which equation has the solution x = 12?

54

7. Ray’s toll pass account has a value of $32. Each time he uses the toll road, $1.25 is deducted from

the account. When the value drops below $10, he must add value to the toll pass. Write an

inequality which represents how many times Ray can use the toll road without having to add value

to the toll pass?

8. The 23 members of the school jazz band are trying to raise at least $1,800 to cover the cost of

traveling to a competition. The members have already raised $750. Which inequality could you use

to find the amount that each member should raise to meet the goal?

9. What is the solution of the inequality 2x – 9 < 7?

10. Max wants to buy some shorts that are priced at $8 each. He decided to buy a pair of sneakers for

$39, but the total cost of the shorts and the sneakers must be less than $75.

Write an inequality for this situation.

Suppose Max wants to buy 6 pairs of shorts. Will he have enough money? Explain.

55

11. A laptop is priced at $475. There is a coupon in the newspaper for 30% off. What is the discount?

What is the sale price? If the sales tax is 8.5% find the total cost of the laptop.

a. Discount Sales Tax

12. 13.

14. 15.

16. 5x + 2(x + 10) = 83 17. 7x + 3(–4x – 5) = – 65

18. 3x + 3(5x – 18) = 108 19. 129 = 2x + 5(2x – 3)